Question

The travel-to-work time for residents of the 15 largest cities in the United States is reported in the 2003 Information Please Almanac. Suppose that a preliminary simple random sample of residents of San Francisco is used to develop a planning value of 6.61 minutes for the population standard deviation.

Round your answers to nearest whole number.

a. If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 5 minutes, what sample size should be used? Assume 95% confidence.

b. If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 2 minutes, what sample size should be used? Assume 95% confidence.

Answer 1

Solution :

Given that,

Population standard deviation = = 6.61 minutes.

a) Margin of error = E = 5 minutes

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z_/2 = Z _0.025 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96 * 6.61 / 5 ]²

n = 6.71

Sample size = n = 7

b) Margin of error = E = 2 minutes.

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96 * 6.61 / 2 ]²

n = 41.96

Sample size = n = 42